Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

PreCal HW Help?

A colony of 2^120 bacteria occupies a total volume of 1.3 times 10^5 meters cubed. The surface area of a planet is approximately 6.84 times 10^14 meters squared.

a. Assume that the bacteria are distributed uniformly over the​ planet's surface. How deep would the bacterial layer​ be? (You can find the approximate depth by dividing the bacteria volume by the​ planet's surface​ area.)

​(Round to the nearest thousandth as​ needed.)

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  • Anonymous
    6 months ago
    Favorite Answer

    < (You can find the approximate depth by dividing the bacteria volume by the​ planet's surface​ area.) >

    Can you divide?

  • 6 months ago

    volume = surface area * deep

    deep = volume / surface area → given that the volume is: 1.3 times 10^(5) m³

    deep = [1.3 * 10^(5)] / surface area → where the surface area is: 6.84 times 10^(14) m²

    deep = [1.3 * 10^(5)] / [6.84 * 10^(14)]

    deep = (1.3/6.84) * [10^(5)/10^(14)]

    deep = (1.3/6.84) * [10^(5) * 10^(- 14)]

    deep = (1.3/6.84) * 10^(5 - 14)

    deep = (1.3/6.84) * 10^(- 9)

    deep ≈ 0.19005848 * 10^(- 9) → rounded

    deep ≈ 0.19006 * 10^(- 9) ← these are meters

    deep ≈ 0.19006 nm ← these are nano-meters

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  • 6 months ago

    You've been recently or at some point in your life introduced to exponents?

    You recognize the numbers given as having to do with exponents?

    1.3×10^5

    -------------

    6.83×10^14

    (1.3 / 6.84) × 10^(5-14)

    0.1903×10^-9

    1.901×10^-10

    In accordance with precision of input data, we round the answer to 1.9×10^-10 m but you can make it thousandths if you really so desire.

    For more practice search "scientific notation" and afterwards make sure you know how to use your calculator.

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  • 6 months ago

    1.3 x 10^5 / (6.84 x 10^14)

    13 x 10^4 / (6.84 x 10^14)

    1.90058 x 10^(-10)

    I would round to 1.9 x 10^(-10) because of significant digits rule.

    To thousandths as requested, 1.901 x 10^(-10)

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  • 6 months ago

    depth = volume/area = 1.3e5 m³ / 6.84e14 m² = 1.901e-10 m

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    • billrussell42
      Lv 7
      6 months agoReport

      that is a decimal value. Perhaps you mean in a different format?

      1.901e-10 m = 1.901x10^-10 m

      but surely you could have done this yourself?

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